SOLUTION: Hi Alex and Blinman have some money. If Alex spends 40 dollars and Belinda spends 80 dollars daily Belinda will have 1250 dollars left when Alex spends all of his money. If Alex s

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Question 1175458: Hi
Alex and Blinman have some money. If Alex spends 40 dollars and Belinda spends 80 dollars daily Belinda will have 1250 dollars left when Alex spends all of his money. If Alex spends 80 dollars and Belinda 40dollars daily Belinda will have 1500 left when Alex has spent all his money.
How much money do Alex and Belinda have.
Thanks
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

Hello, your message REQUIRES two corrections in order for it makes sense.

First, the name Blinman in the first line must be changed by Belinda.
It is OBVIOUS and does not require explanation.

Second, the number 1250 in your message must be changed to 1260, in order for the numbers in the solution be integer
(as you will see from my solution below).

So, I transform your text this way 

    Alex and Belinda have some money. 
    If Alex spends 40 dollars and Belinda spends 80 dollars daily Belinda will have 1260 dollars left when Alex spends all of his money. 
    If Alex spends 80 dollars and Belinda 40dollars daily Belinda will have 1500 left when Alex has spent all his money. 
    How much money do Alex and Belinda have.


                    Solution


This problem is special.
Usually, setuping for standard word problems is easy and routine task, but not in this case.
This problem is non-standard, therefore, setuping may perplex an average student.
It makes this problem interesting. 

Let A be the amount that Alex has and B be the amount that Belinda has.

Let "d" be the number of days in the 1-st scenario and "t" be the number of days in the second scenario.


Then we can write these equations


    A = 40d,            (1)

    B - 80d = 1260,     (2)

    A = 80t,            (3)

    B - 40t = 1500.     (4)


We have 4 equations for 4 unknown, so the problem is dowable.


Comparing equations (1) and (3), we see that  d = 2t.  Substitute  d = 2t into equations (2) and (3).  You will get


    B - 80*(2t) = 1260     

    B - 40*t    = 1500      

or

    B -  160t   = 1260    (5) 

    B -   40t   = 1500    (6)


Subtracting equation (5) from equation (6), you get

         120t   = 240,

hence       t   = 240/120 = 2.    


Now we easy find  A = 80*2 = 160  from (3),  and  B = 1500 + 40*2 = 1580  from (4).


ANSWER.  A has 160 dollars;  B has 1580 dollars.

Solved.



Answer by Edwin McCravy(20056) About Me  (Show Source):